Dasymetric models increase the spatial resolution of population data by incorporating related ancillary data layers. The role of uncertainty in dasymetric modeling has not been fully addressed as of yet. Uncertainty is usually present because most population data are themselves uncertain, or the geographic processes that connect population and the ancillary data layers are not precisely known. A new dasymetric methodology—the penalized maximum entropy dasymetric model (P–MEDM)—is presented that enables these sources of uncertainty to be represented and modeled. The P–MEDM propagates uncertainty through the model and yields fine-resolution population estimates with associated measures of uncertainty. This methodology contains a number of other benefits of theoretical and practical interest. In dasymetric modeling, researchers often struggle with identifying a relationship between population and ancillary data layers. The P–MEDM model simplifies this step by unifying how ancillary data are included. The P–MEDM also allows a rich array of data to be included, with disparate spatial resolutions, attribute resolutions, and uncertainties. Although the P–MEDM does not necessarily produce more precise estimates than do existing approaches, it does help to unify how data enter the dasymetric model, it increases the types of data that can be used, and it allows geographers to characterize the quality of their dasymetric estimates. We present an application of the P–MEDM that includes household-level survey data combined with higher spatial resolution data such as from census tracts, block groups, and land cover classifications.

Terrain is modelled in Geographic Information Science on a grid, assuming that elevation values are constant within any single pixel of a Digital Elevation Model (DEM). Pixels are considered flat and rigid, for computational simplicity (a ‘rigid pixel’ paradigm). This paradigm does not account for the slope and curvature of terrain within each pixel, generating imprecise measurements, particularly as pixel size increases or in uneven terrain. This paper relaxes the rigid pixel assumption, allowing for possible sub-pixel variations in slope and curvature (a ‘surface-adjusted’ paradigm). This paper compares different interpolation methods to investigate sub-pixel variations for estimating elevation of arbitrary points given a regular grid. Tests interpolating elevation values for 20,000 georeferenced off-centroid random points from a regular grid DEM are presented, using a variety of exact and inexact local deterministic interpolation methods within contiguity configurations incorporating first and second order neighbours. The paper examines the accuracy of surface-adjusted estimations across a progression of spatial resolutions (10 m, 30 m, 100 m, and 1,000 m DEMs) and a suite of terrain types varying in latitude, altitude, slope, and roughness, validating off-centre estimates against direct elevation measurements on 3 m resolution lidar DEM. Results illustrate that the Bi-quadratic and Bi-cubic interpolation methods outperform Weighted Average, Linear, and Bi-linear methods at coarse resolutions and in rough or non-uniform terrain. In smooth or flat terrain and at finest resolutions, the interpolation method impacts estimation accuracy less or not at all. The type of contiguity configuration appears to play a role in estimation errors as well, with tighter neighbourhoods exhibiting higher accuracy. The analysis also examined regularized mathematical surfaces, adding autocorrelated randomly distributed noise to simulate terrain. The results of experiments based on regularized smooth mathematical surfaces do not translate directly to terrain modelling. The analysis also considers the balance between the increased computation times needed to measure surface-adjusted elevation against improvements in accuracy.

Comparability among population data enumerated within different time periods may be complicated by changing enumeration boundaries over time. Areal interpolation methods are commonly used to solve such zoning incompatibilities, but are frequently based on the questionable assumption of homogeneous population density within the different zones. To achieve more accurate estimates, land cover or other ancillary data may be used to better characterize the underlying source zone population density surface prior to areal interpolation. Although dasymetric techniques such as these are well documented, their effectiveness across different areal interpolation methods are not well established. This research compares the accuracy of a number of areal interpolation methods used to support temporal analysis of population data, and evaluates the effect of dasymetric mapping on interpolation accuracy. Our findings demonstrate that dasymetric refinement noticeably improves interpolation accuracy for the areal weighting, pycnophylactic, and target density weighting (TDW) methods of areal interpolation. A fourth method in which land cover densities are inherently incorporated, the expectation–maximization algorithm (EM), performs equally well. Our results show that the dasymetrically refined TDW method outperforms other areal interpolation methods in most instances, but suggest that the EM algorithm may be preferred as the interval between enumeration periods grows large.